The Brennan–Lomasky Test of Expressive Voting: When Impressive Probability Differences Are Meaningless

We consider a test of expressive voting developed by Brennan and Lomasky (1993). They point out that in presidential elections the probability of a tie, and casting a decisive vote, increases “multi-billionfold” as the election becomes increasingly close. They conjecture that if voters are instrumentally motivated there would be enormous increases in voter turnout for presidential elections as they became close. When they find no consistent relationship between closeness and turnout in presidential elections since 1940, they conclude their test justifies a “decisive rejection of the instrumental voter hypothesis.” As dramatic as such a “multi-billionfold” increase is, we argue it would not motivate voting if an instrumental payoff was the only motivation for doing so. The Brennan–Lomasky test does give the correct result, but not for the reason they emphasize. They do see reasons why voting turnout would be moderated other than the dramatic probability of a decisive vote in close elections. Furthermore, they close their test by indicating that one reason turnout might be higher in close elections is that they are more interesting, which is congenial to an expressive account. We agree. We also argue that the observed tendency for voters to confirm their biases rather than change their minds provides additional support for expressive voting.

Onze débats télévisés pour une campagne présidentielle

Since 1974 the second-round debate has been an obligatory fixture in the calendar for French presidential candidates. In 2017 this traditional debate was joined by ten others: eight for the primaries, extended for the first time to the Right (three first-round debates and one before the decisive vote for each side of the political spectrum). There were also two debates before the first round of voting in the presidential election itself. A debate can be defined as an interactive mode of communication based on an exchange of arguments embedded within a unidirectional system of communication (a TV broadcast). Different types of categories have been used to analyse candidates’ exchanges in these debates, identifying divergence and convergence, retrospective or prospective discourses, whether a message is aggressive or defensive, and whether it is policy-orientated or relational in scope.

Electoral Competition and Redistribution with Rationally Informed Voters

In spite of the negligible probability that everyone has to cast a decisive vote, political information can be relevant for a number of private decisions. Under quite mild assumptions, the demand for information is increasing in income. Being informed affects responsiveness to electoral platforms and vote-seeking political parties should take this into account in their optimization process. As a consequence, redistribution is generally lower than what the median voter theorem predicts. Moreover, in contrast with what most literature takes for granted, an increase in inequality does not unambiguously increase redistribution. This is consistent with most empirical research in this field. Finally, an increase in the cost of information induces a reduction in redistribution.

Standard Voting Power Indexes Do Not Work: An Empirical Analysis

Voting power indexes such as that of Banzhaf are derived, explicitly or implicitly, from the assumption that all votes are equally likely (i.e., random voting). That assumption implies that the probability of a vote being decisive in a jurisdiction with n voters is proportional to 1/√n. In this article the authors show how this hypothesis has been empirically tested and rejected using data from various US and European elections. They find that the probability of a decisive vote is approximately proportional to 1/n. The random voting model (and, more generally, the square-root rule) overestimates the probability of close elections in larger jurisdictions. As a result, classical voting power indexes make voters in large jurisdictions appear more powerful than they really are. The most important political implication of their result is that proportionally weighted voting systems (that is, each jurisdiction gets a number of votes proportional to n) are basically fair. This contradicts the claim in the voting power literature that weights should be approximately proportional to √n.